Palace lost their first seven games of the season but are now five points clear of safety and Hodgson said: "We can look at the league table for a week or two without shivers running down our spine".
However, their comments have acquired more bite lately, beginning when Mourinho implied that Conte was a "clown" for his dramatic touchline celebrations, although he later claimed he was not referring specifically to the Italian.
Mourinho and the Chelsea boss have been trading verbal blows over the last month and that continued last week when Conte labelled the United manager "a little man" after his side's FA Cup 0-0 draw against Norwich City.
However, the best Chelsea could manage were harmless long-range strikes from N'Golo Kante and Marcos Alonso as Leicester held firm to leave Conte grumbling his way down the tunnel at full-time.
While they will be hoping to cause havoc in the final third, Gary Cahill has been drafted back in to a defensive unit seeking to keep the Foxes out. We played the game against Arsenal on Wednesday night and didn't have a lot of time to recover.
But Conte is adamant Morata isn't the only one to blame for Chelsea's profligacy.
Despite David Luiz being on the bench, Antonio Conte chose Andreas Christensen as the man to replace the England worldwide.
Antonio Conte and Chelsea made unwanted history following Saturday's stalemate against Leicester City.
Leicester were relentless, playing like champions, with the intensity of their pressing forcing mistakes, but Ben Chilwell was sent off for two bookable offences in quick succession, leaving the visitors down to 10 men with 22 minutes remaining.
Conte said: "Everyone is frustrated after another 0-0".
The Foxes had the better of the chances and Antonio Conte reacted by replacing Eden Hazard, ineffectual with Leicester's intense closing down robbing him of service, and Cesc Fabregas with Willian and Pedro before the hour mark. He says what system we use does not make a difference at the moment.
I never see this type of mistake in the Premier League before.